The team didn't announce a timeline for Calhoun's return.
The 33-year-old recently went for an MRI due to right knee inflammation, manager Torey Lovullo told Zach Buchanan of The Athletic.
He was projected to open the season as Arizona's starting right fielder.
Calhoun is entering the second season of a two-year, $16-million contract with the Diamondbacks. He hit .226/.338/.526 with 16 home runs and 40 RBIs in 54 games last season.